Astrophysical Particle Simulations with Custom GPU Clusters

We present our new parallel GPU clusters in Beijing and Heidelberg and demonstrate the nearly optimal speedup and performance for parallel direct astrophysical N-body simulations with up to six million bodies. We reach about 1/3 of the peak performance for a real application code. The clusters are used to simulate dense star clusters with many binaries and galactic nuclei with supermassive black holes, in which correlations between distant particles cannot be neglected.

[1]  P. Kroupa,et al.  SUPERBOX – an efficient code for collisionless galactic dynamics , 2000 .

[2]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[3]  Toshiyuki Fukushige,et al.  GreeM: Massively Parallel TreePM Code for Large Cosmological N-body Simulations , 2009, 0910.0121.

[4]  R. Spurzem.  Direct N-body simulations , 1999, astro-ph/9906154.

[5]  Rainer Spurzem,et al.  Parallelization, Special Hardware and Post-Newtonian Dynamics in Direct N - Body Simulations , 2008 .

[6]  Leonid Oliker.  Green flash: Designing an energy efficient climate supercomputer , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[7]  Guillermo Marcus Martinez,et al.  Accelerating astrophysical particle simulations with programmable hardware (FPGA and GPU) , 2009, Computer Science - Research and Development.

[8]  Toshiyuki Fukushige,et al.  GRAPE-6: Massively-Parallel Special-Purpose Computer for Astrophysical Particle Simulations , 2003, astro-ph/0310702.

[9]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[10]  Toshiyuki Fukushige,et al.  PPPM and TreePM Methods on GRAPE Systems for Cosmological N-body Simulations , 2005 .

[11]  Christopher J. Fluke,et al.  Teraflop per second gravitational lensing ray-shooting using graphics processing units , 2009, 0905.2453.

[12]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[13]  H.M.P. Couchman,et al.  Hydra: a parallel adaptive grid code , 1997 .

[14]  Robert G. Belleman,et al.  High Performance Direct Gravitational N-body Simulations on Graphics Processing Units , 2007, ArXiv.

[15]  Christopher J. Fluke,et al.  Advanced Architectures for Astrophysical Supercomputing , 2010, 1001.2048.

[16]  N. Nakasato,et al.  Oct-tree Method on GPU , 2010 .

[17]  Andreas Burkert,et al.  Special, hardware accelerated, parallel SPH code for galaxy evolution. , 2007 .

[18]  Junichiro Makino,et al.  Performance analysis of direct N-body calculations , 1988 .

[19]  Guohong Xu.  A new parallel N body gravity solver: TPM , 1994, astro-ph/9409021.

[20]  Junichiro Makino,et al.  A Fast Parallel Treecode with GRAPE , 2004 .

[21]  Walter Dehnen,et al.  A Hierarchical O(N) Force Calculation Algorithm , 2002 .

[22]  Edward K. Porter,et al.  Binaries of massive black holes in rotating clusters: Dynamics, gravitational waves, detection and the role of eccentricity , 2009, 0908.0755.

[23]  Emil Khalisi,et al.  A comprehensive nbody study of mass segregation in star clusters: energy equipartition and escape , 2006, astro-ph/0602570.

[24]  J. Makino,et al.  GRAPE-6A: A Single-Card GRAPE-6 for Parallel PC-GRAPE Cluster Systems , 2005, astro-ph/0504407.

[25]  Zesheng Tang,et al.  Efficient magnetohydrodynamic simulations on graphics processing units with CUDA , 2009, Comput. Phys. Commun..

[26]  Koji Yasuda,et al.  Two‐electron integral evaluation on the graphics processor unit , 2008, J. Comput. Chem..

[27]  Tzihong Chiueh,et al.  GAMER: A GRAPHIC PROCESSING UNIT ACCELERATED ADAPTIVE-MESH-REFINEMENT CODE FOR ASTROPHYSICS , 2009, 0907.3390.

[28]  Reinhard Männer,et al.  From Newton to Einstein ? N-body dynamics in galactic nuclei and SPH using new special hardware and astrogrid-D , 2007 .

[29]  D. Merritt,et al.  Performance Analysis of Direct N-Body Algorithms on Special-Purpose Supercomputers , 2006, astro-ph/0608125.

[30]  V. Springel.  The Cosmological simulation code GADGET-2 , 2005, astro-ph/0505010.

[31]  F. Pearce,et al.  Hydra: An Adaptive--Mesh Implementation of PPPM--SPH , 1994 .

[32]  Junichiro Makino,et al.  Triplets of supermassive black holes: Astrophysics, Gravitational Waves and Detection , 2009, 0910.1587.

[33]  J. Makino,et al.  Sixth- and eighth-order Hermite integrator for N-body simulations , 2007, 0708.0738.

[34]  Junichiro Makino,et al.  On a Hermite Integrator with Ahmad-Cohen Scheme for Gravitational Many-Body Problems , 1992 .

[35]  Peng Wang,et al.  Adaptive mesh fluid simulations on GPU , 2009, 0910.5547.

[36]  Dehnen.  A Very Fast and Momentum-conserving Tree Code. , 2000, The Astrophysical journal.

[37]  Simon Portegies Zwart,et al.  High-performance direct gravitational N-body simulations on graphics processing units , 2007, astro-ph/0702058.

[38]  Yunfei Chen,et al.  GPU accelerated molecular dynamics simulation of thermal conductivities , 2007, J. Comput. Phys..

[39]  P. Amaro-Seoane,et al.  Physical Processes in Star–Gas Systems , 2004, Publications of the Astronomical Society of Australia.